The pier at Yorktown beach isn't the friendliest for fishing. If you go across the Coleman bridge (the big bridge over the York river), there is a pier a Gloucester Point that is more fishing oriented.
There is also a pier at Croaker Landing at the York River State Park -- I launch from there and often have room for a guest or two on my boat, so PM me if you're interested.
In June on the York expect to catch Croaker, Spot & Blue Crabs.